Yeah, it looks like it's the absolute path; those don't really work in my experience with DX. Have to go the old Shell Object route. Try this one:
Const DESKTOP = &H10&
Set objShell = CreateObject("Shell.Application")
Set objFolder = objShell.Namespace(DESKTOP)
Set objFolderItem = objFolder.Self
Dim desktoppath : desktoppath = objFolderItem.Path
Sub Object_OnLButtonDown(x,y)
System.DownloadFile "http://siteweb.com/downloads/icons/icons.gif", desktoppath &"\icons.gif", True
End Sub